développer expan(1+4x)^7

Solution

développer

e x p an (1 + 4 x)^{7}

e n x p a + 28 e n x^{2} p a + 336 e n x^{3} p a + 2240 e n x^{4} p a + 8960 e n x^{5} p a + 21504 e n x^{6} p a + 28672 e n x^{7} p a + 16384 e n x^{8} p a

étapes des solutions

e x p an (1 + 4 x)^{7}

(1 + 4 x)^{7} = 1 + 28 x + 336 x^{2} + 2240 x^{3} + 8960 x^{4} + 21504 x^{5} + 28672 x^{6} + 16384 x^{7}

= e n x p a (16384 x^{7} + 28672 x^{6} + 21504 x^{5} + 8960 x^{4} + 2240 x^{3} + 336 x^{2} + 28 x + 1)

= e n x p a (1 + 28 x + 336 x^{2} + 2240 x^{3} + 8960 x^{4} + 21504 x^{5} + 28672 x^{6} + 16384 x^{7})

Distribuer des parenthèses

= e x p an \cdot 1 + e x p an \cdot 28 x + e x p an \cdot 336 x^{2} + e x p an \cdot 2240 x^{3} + e x p an \cdot 8960 x^{4} + e x p an \cdot 21504 x^{5} + e x p an \cdot 28672 x^{6} + e x p an \cdot 16384 x^{7}

= 1 e n x p a + 28 e n xx p a + 336 e n x^{2} x p a + 2240 e n x^{3} x p a + 8960 e n x^{4} x p a + 21504 e n x^{5} x p a + 28672 e n x^{6} x p a + 16384 e n x^{7} x p a

Simplifier

1 e n x p a + 28 e n xx p a + 336 e n x^{2} x p a + 2240 e n x^{3} x p a + 8960 e n x^{4} x p a + 21504 e n x^{5} x p a + 28672 e n x^{6} x p a + 16384 e n x^{7} x p a : e n x p a + 28 e n x^{2} p a + 336 e n x^{3} p a + 2240 e n x^{4} p a + 8960 e n x^{5} p a + 21504 e n x^{6} p a + 28672 e n x^{7} p a + 16384 e n x^{8} p a

= e n x p a + 28 e n x^{2} p a + 336 e n x^{3} p a + 2240 e n x^{4} p a + 8960 e n x^{5} p a + 21504 e n x^{6} p a + 28672 e n x^{7} p a + 16384 e n x^{8} p a

e x p an d (x - 2) (y^{2} + 25) d x

e x p an d so l v e (π \cdot r^{2} + π \cdot r \cdot 5.4 = 46.5, r)

e x p an d \frac{3}{( z - 1 ) ( z + 2 )}

e x p an d n^{2 (n - m + 1)}

e x p an d (- 4 x, - 1, 2 y + 1) \cdot (0, 2, 1)